Luciano Spalletti's side missed the opportunity to extend their one-point lead at the summit - ahead of their title rivals playing later in the weekend - as a pair of Davide Santon errors contributed to the coach's first competitive loss at the helm and ended their 16-game undefeated match in Serie A this term.
Kevin Lasagna cooked up a scarcely deserved opener that was cancelled out by Mauro Icardi's 17th league goal of the season just 72 seconds later, but Inter - back at full strength after a midweek Coppa Italia scare against Pordenone - failed to turn their dominance into a crucial second.
Instead, Udinese grew in confidence after the interval and Santon's handball – only penalised after the use of VAR by referee Maurizio Mariani – allowed Rodrigo De Paul to send a penalty past Samir Handanovic.
Milan Skriniar came close to restoring parity when he hit the woodwork, but Udinese took full advantage of the hosts' increasing desperation and clinched victory on the counter-attack with Antonin Barak's strike 13 minutes from time.
Napoli can now leapfrog Inter with victory at Torino later on Saturday, while Spalletti's men will end the weekend in third if Juventus also win at Bologna on Sunday.
Inter predictably found early joy in wide areas, but Matias Vecino, Antonio Candreva and Ivan Perisic all failed to make the most of their team-mates' dangerous deliveries.
And the hosts were made to pay for their profligacy. Santon cheaply gave up possession to Silvan Widmer, who danced past a couple of weak challenges in the area and centred for Lasagna to convert.
But the response was swift and Icardi took just over a minute to draw his side level, reaching Candreva's right-wing cross to turn a low finish past Albano Bizzarri.
Inter pushed for a second goal, altering their approach to pepper Bizzarri with strikes from distance; two fizzing efforts from Candreva and Marcelo Brozovic only narrowly missed the target.
The Udinese goalkeeper stood up well to a Perisic drive and then similarly parried away Candreva's next attempt on the stroke of half-time.
Lasagna should have restored the visitors' lead just 31 seconds after the restart, instead failing to hit the target when Skriniar's uncharacteristically sloppy defending served up a golden opportunity inside the six-yard box.
Icardi nodded over the top at the other end, but Udinese's improved second-half showing continued and – after referee Mariani reviewed video footage to deem that the ball did not cross the byline before Santon handled a cross from Widmer – De Paul ruthlessly dispatched from the spot.
Inter kicked on again but toiled in front of goal once more, with Skriniar angling a header against the crossbar and Bizzarri keeping out Roberto Gagliardini's effort.
But the pressure on the Udinese goal left gaps at the other end and Barak pounced from Jakub Jankto's cross to stun Spalletti's men with a third, putting their place at the summit under threat.
